When radio signals are being transmitted between a transmitter and a receiver, various interference influences occur which have to be taken into account during the signal detection process at the receiver end. Firstly, the signal is subject to distortion that is caused because there are generally two or more possible signal propagation paths. Owing to reflection, scatter and diffraction of signal waves of obstructions, such as buildings, mountains and the like, the reception field strength of the receiver is composed of two or more signal components which generally have different strengths and are subject to different delays. This phenomenon, which is referred to as multipath propagation, causes the transmitted data signal distortion that is known as intersymbol interference (ISI).
Other active subscribers represent a further cause of interference. The interference that is caused by these subscribers is referred to as multi access interference: MAI.
First of all, only one channel will be considered, that is to say MAI will be ignored. This multipath transmission channel between the transmitter S and the receiver E can be modelled as a transmission filter H with channel coefficients hk as is illustrated in FIG. 1. The transmitter S feeds transmission symbols sk into the transmission channel, that is to say the channel model transmission filter H. A model adder SU allows an additive noise contribution nk to be taken into account, which is added to the transmission symbols sk, which have been filtered with hk, at the output of the channel model transmission filter H.
The index k denotes the discrete time in time limits of the symbol clock rate. The transmission signals sk, which have been filtered by the transmission filter H and on which noise has been superimposed are received as the received signal xk by the receiver E, as follows:
                              x          k                =                                            ∑                              i                =                0                            L                        ⁢                                          h                i                            ⁢                              s                                  k                  -                  i                                                              +                      n            k                                              (        1        )            where L represents the order of the transmission channel which is modelled by the filter H. As can be seen from equation 1, ISI is present, since xk depends not only on sk but also on sk−1, . . . , sk−L.
FIG. 2 shows the channel model transmission filter H. The filter H is formed by a shift register comprising L memory cells Z. Taps (a total of L+1 of them) are in each case located in front of and behind each memory cell Z and lead to multipliers, which multiply the values of the symbols sk, Sk−1, . . . , sk−L, which are inserted into the shift register via an input IN at the symbol clock rate T−1, by the corresponding channel impulse responses h0, h1, . . . hL. An output stage AD of the filter H adds the outputs of the L+1 multipliers. This thus results in an output signal OUT as in equation 1.
The memory content of the channel model shift register describes the state of the channel. The memory content of the first memory cell on the input side contains the symbol sk−1 (which is multiplied by h1) in the time unit k, and the other memory cells Z are occupied by the symbols sk−2, sk−3, . . . , Sk−L. The state of the channel in the time unit k is thus uniquely governed by the details of the memory contents, that is to say by the L-tuple (sk−L, Sk−L+1, . . . Sk−1).
In the receiver E, the received signal values xk are known as sample values, and the channel impulse responses h0, h1, . . . , hL for the channel are estimated at regular time intervals. The equalization task comprises the calculation of the transmission symbols sk from this information. The following text considers the equalization process by means of a Viterbi equalizer.
Viterbi equalization is based on finding the shortest path through a state diagram for the channel, and this is referred to as a trellis diagram. The channel states are plotted against the discrete time k in the trellis diagram. According to the Viterbi algorithm (VA), a branch metric, which represents a measure of the probability of the transition, is calculated for each possible transition between two states (previous state relating to the time unit k, destination state relating to the time unit k+1). The branch metrics are then added to the respective state metrics (which are frequently also referred to in the literature as path metrics) of the previous states (ADD). In the case of transitions to the same destination state, the sums obtained in this way are compared (COMPARE). That transition to the destination state under consideration whose sum of the branch metric and state metric of the previous state is the minimum is selected (SELECT) and forms the extension of the path leading into this previous state to the destination state. These three basic operations of the VA are known as ACS (ADD-COMPARE-SELECT) operations.
While, from the combinational point of view, the number of paths through the trellis diagram increases exponentially as k increases (that is to say as time progresses), the number remains constant for VA. This is because of the selection step (SELECT). Only the selected path (survivor) survives and can be continued further. The other possible paths are rejected. The recursive path rejection process is the fundamental concept of the VA and is an essential precondition for using calculations to solve the problem of searching for the shortest path (also referred to as the best path) through the trellis diagram.
The number of channel states (that is to say the number of occupancy options in the shift register H) in the trellis diagram is mL, and this is identical to the number of paths that are followed through the trellis diagram. In this case, m denotes the significance of the data symbols under consideration. The computation complexity for the VA accordingly increases exponentially with L. Since L should correspond to the length of the channel memory of the physical propagation channel, the complexity for processing the trellis diagram increases as the channel memory of the physical propagation channel rises.
One simple method to reduce the computation complexity is to base the trellis processing on a short channel memory L of, for example, 2 or 3 time units (taps). However, this has a major adverse effect on the performance of the equalizer. The decision feedback method (DF) is a considerably more worthwhile measure for limiting the computation complexity, and does not have a serious influence on the quality of the equalizer. In the case of the DF method, the VA is based on a reduced trellis diagram, that is to say a trellis diagram in which only some of the mL channel states are considered, rather than all of them. If the trellis diagram is reduced to mLDF trellis states (LDF<L) the remaining L−LDF channel coefficients (which are not used for the definition of trellis states) are still considered by being used for the calculation of the branch metrics in the reduced trellis diagram.
A branch metric must be calculated for each possible transition between two states, both during the processing of the complete trellis diagram and during processing of the reduced trellis diagram (DF case). The branch metric is the Euclidean distance between the measured signal value or sample value xk and a reconstructed “hypothetical” signal value which is calculated and “tested” in the receiver for the destination state, the transition from previous state to the destination state and for the path history taking account of the channel knowledge.
By way of example, m is assumed to be equal to 2 (binary data signal), that is to say there are 2L (DF case: 2LDF) trellis states (0, 0, . . . , 0), (1, 0, . . . , 0) to (1, 1, . . . , 1) comprising L tuples (DF: LDF tuples). One specific hypothetical previous state is assumed to be defined by the shift register occupancy (aL, aL−1, . . . , a1) (only the LDF right-hand bits (aLDF, . . . , a1) of the shift register occupancy are used for the state definition DF case). a0 denotes the hypothetically transmitted symbol (bit) 0 or 1 which changes the previous state (aL,aL−1, . . . , a1) for the time unit k to the destination state (aL−1, aL−2, . . . , a0) for the time unit k+1 (DF: previous state (aLDF, . . . , a1) to the destination state (aLDF−1, . . . , a0)). The branch metric BMk, with or without DF, is:
                              BM          k                =                ⁢                                                                        Sample  value                            -                              reconstructed  signal  value                                                          2                                        =                ⁢                                                                        x                k                            -                              (                                                                            ∑                                              i                        =                        1                                            L                                        ⁢                                                                  h                        i                                            ⁡                                              (                                                  1                          -                                                      2                            ·                                                          a                              i                                                                                                      )                                                                              +                                                            h                      0                                        ⁡                                          (                                              1                        -                                                  2                          ·                                                      a                            0                                                                                              )                                                                      )                                                          2                    for ai={0, 1}(2)
The reconstructed signal value (which is also referred to in the following text as the reconstructed symbol) is a sum of products of a channel coefficient and a symbol. For the DF case, the term
      ∑          i      =      1        L    ⁢            h      i        ⁡          (              1        -                  2          ·                      a            i                              )      can also be split into a trellis contribution and a DF contribution:
                              BM          k                =                                                                        x                k                            -                              (                                                                                                    ∑                                                  i                          =                                                                                    L                              DF                                                        +                            1                                                                          L                                            ⁢                                                                        h                          i                                                ⁡                                                  (                                                      1                            -                                                          2                              ·                                                              a                                i                                                                                                              )                                                                                                            ︸                                              DF                        ⁢                                                                                                  ⁢                        contribution                                                                              +                                                                                    ∑                                                  i                          =                          1                                                                          L                          DF                                                                    ⁢                                                                        h                          i                                                ⁡                                                  (                                                      1                            -                                                          2                              ·                                                              a                                i                                                                                                              )                                                                                                            ︸                                              Trellis                        ⁢                                                                                                  ⁢                        contribution                                                                              +                                                                                    h                        0                                            ⁡                                              (                                                  1                          -                                                      2                            ·                                                          a                              0                                                                                                      )                                                                                    ︸                                                                                                                                  hyp                              .                                                                                                                          ⁢                              symbol                                                                                                                                                            contribution                                                                                                                                              )                                                          2                                    (        3        )            
This means that the reconstructed symbol comprises two (DF case: three) contributions: a contribution which is governed by the hypothetically transmitted symbol a0 for the transition from the time unit k to the time unit k+1, the trellis contribution which is given by the previous state relating to the time unit k in the trellis diagram, and, in the case of DF, there is also the DF contribution which results from the reduced trellis states.
The branch metric BMk is always the same, with or without DF. The computation saving VA with DF results, as already mentioned, from the smaller number 2LDF of trellis states to be considered for the processing of the trellis diagram, that is to say from the reduction of the trellis diagram.
If it is also intended to take account of an interference channel (that is to say a second multipath transmission channel) in the equalization of a data signal, both channels (the data channel and the interference channel) must be subjected to VA equalization jointly. An overall trellis diagram that includes the states for both channels is constructed for this purpose. FIG. 3 shows an example of an overall trellis diagram such as this for m=2 (binary data signal) and L=2 for both channels. The trellis diagram for each individual channel in this case has (only) 4 states. The “combinational” overall trellis diagram on which the joint VA equalization of both signals is based comprises 4×4=16 states. Each state of the overall trellis diagram is represented by 4 bits, with the bits for the user and for the interference source being indicated alternately in FIG. 3 in order to define an overall state (combined user/interference source state). 4 transitions leave one state of the overall trellis diagram, and 4 transitions lead to each state in the overall trellis diagram. The transitions that lead to the combined states 0, 0, 0, 0, 0, 0, 1, 0 and 1, 1, 0, 0, 1, 1, 1, 0 are illustrated in FIG. 1. The four transitions are each composed of two transitions from the individual trellis diagrams.
If a further interference source is added, the overall trellis diagram already comprises 4×4×4=64 states (m=L=2 is likewise assumed for the other interference source). At the latest when a channel memory of L>2 is taken account of for each channel, the computation complexity rises to such an extent that conventional VA equalization of the overall trellis diagram is no longer possible.